Iran's vice-president has said that the phone conversation between Hassan Rouhani and Barack Obama was of huge global significance and represented a defeat for hardliners in both countries.

Writing for the Guardian, Masoumeh Ebtekar, a vice-president to Rouhani, called on the US administration not to repeat the missed opportunities during Iran's reformist mandate more than a decade ago, which she said cost countless lives in wars in the Middle East.

"These leaders came with a mandate to negotiate and demonstrated their desire to do so with the first presidential telephone conversation between the two sides since 1979. That might appear insignificant, but was of huge global political importance," Ebtekar wrote after Rouhani's return to Tehran from New York.

"This development on both sides succeeded despite strong pressure from hardliners and those looking backward instead of forward within the political context of their respective nations."

Rouhani has been broadly praised at home for his UN visit while hawkish hardliners have largely held back from criticism because the president is assumed to have the backing of Iran's supreme leader, Ali Khamenei, for the overture with the US.

Iran's conservative-dominated parliament also endorsed the president's visit, local agencies said on Wednesday, reporting that the speaker, Ali Larijani, had praised the president on the visit.

Ebtekar, who is the head of Iran's environmental protection organisation, said the standoff between Tehran and the west over Iran's nuclear programme and the Syrian conflict are two contemporary challenges that need to be addressed urgently. But she warned that the Tehran-Washington rapprochement, which has increased hopes for a breakthrough, would not bear fruit unless the US showed consistency in its words and actions.

"President Obama also indicated that the US does not seek regime change in Tehran and that the two countries can have a different, more open relationship after the dispute is settled," she writes. "While the US seems ready to reciprocate, many observers question whether all the elements of the US administration are pulling in the same direction and whether there will be practical confidence-building measures in the near future to consolidate the fruits of this visit."

Ebtekar's warning comes after Obama reassured Israel's prime minister, Benjamin Netanyahu, that the military option against Tehran has not been taken off the table.

There is also scepticism whether Obama can reciprocate any Iranian compromise in the face of fierce resistance from Congress. Following Obama's conversation with Netanyahu earlier this week, Iran's foreign minister, Mohammad Javad Zarif, tweeted on Tuesday that the US needed a consistent policy with Iran. "President Obama needs consistency to promote mutual confidence. Flip flop destroys trust and undermines US credibility," he said.

In her article, Ebtekar recalls previous missed opportunities to improve US-Iran relations under the reformist administration of Mohammad Khatami between 1997 to 2005. She urged the west to seize the opportunity created by Rouhani, whom she said has unrestricted mandate to resolve the dispute over Iran's nuclear activities.

"In 1998, when President Khatami came to the UN with the novel approach of dialogue among civilisations, he faced an unrelenting storm of internal pressure while the US president branded Iran a member of the axis of evil, thus neutralising his excellent initiative at both the domestic and global levels," she recalls. "With the passage of 15 years and the loss of millions of lives in global wars, perhaps we have all learned our lesson and global leaders are more prepared to say no to militarism, terrorism, nuclear arsenals and extremism."

Ebtekar, 53, spent at least six years of her childhood in the US but later became involved in Iran's 1979 Islamic revolution.Because of her English-language skills, she became a spokeswoman for the students who stormed the US embassy in Tehran and took 52 diplomats hostage for 444 days. At the time she was nicknamed Mary. She later sided with the reformists and under Khatami was appointed the Islamic republic's first female vice-president.

Ebtekar was marginalised under Ahmadinejad and came under fire in the aftermath of the disputed 2009 election when she visited victims of the popular uprising.

In her article, Ebtekar says Rouhani's election has raised hopes for an internal opening towards political prisoners, many of whom were arrested in 2009.

"There has been gradual release of political prisoners who were detained on grounds of opposition to the results of the controversial elections of 2009," she writes. "This demonstrates a unified and genuine effort on behalf of Iran to change the political atmosphere while adhering to the basic precepts and principles of the Islamic Republic and the inalienable right of Iran to enrich uranium for peaceful purposes."

Prior to Rouhani's visit to New York, local agencies said Khamenei had declared amnesty for 80 political prisoners, boosting the president's credibility but activists have been so far unable to fully identify them.

Despite Ebtekar's comments, there is confusion in Tehran whether Rouhani's decision to speak to Obama was made with or without Khamenei's knowledge. This was reinforced when the commander of the elite revolutionary guards, the shock troopers of Iranian power, said earlier in the week that he approved the president's manoeuvres in New York but considered his conversation with Obama premature. Conservative media, including the Kayhan newspaper, have also shown dissatisfaction with the phone call.